DE-OS No. 33 38 493 discloses a method and a device for splicing glass fiber bundles. In that method, the glass fibers of the ends of two bundles which have previously bee prepared for splicing are each placed and fixed in parallel V-shaped grooves of an axially and laterally movable supporting plate so that the fiber ends overlap, a glass fiber of one bundle and a glass fiber of the other bundle alternately lying side by side in each supporting plate. The glass fibers are releasably fixed in the splicing device by means of holding-down devices which are placed above the glass fibers and which press them into the grooves of the supporting plates. Minor manufacturing variations of the diameter of the glass fibers are compensated for by the design of the holding-down device as an elastic cushion. However, the adhesion produced between the pressed-down cushion and the grooves when the glass fibers are fixed is often not strong enough to safely protect the glass fibers in the splicing device from axial displacements. Such protection is necessary, however, because the end faces of the fibers must have exact 90.degree. fractures before being welded. The fractures are made with a scoring tool which is moved within the splicing device across the glass fibers transverse to the axial direction. Tensile action on the glass fibers after scoring will result in such smooth 90.degree. fractures.